Stability Analysis Of An Epidemic Model With“Healthy Carriers”

Prevention and control of infectious diseases is a major issue related to human health and the national economy. The quantitative study is a popular rule and an important basis for the disease prevention and control. For a long time, human are struggle with the diseases.for example, Smallpox eradication, leprosy, polio has been eradicated around the corner,The advent of multiple antibiotics. Such as the 1922 England bacteriologist Alexander Fleming( Alexander.Fleming, 1881-1955) discovered penicillin saved thousands of lives.However,the World Health Report published by World Health Organization(WHO) shows that infectious disease is still the number one killer of mankind.The ?rst part of this paper is the introduction, describes some of the models have healthy carriers of the disease and research background, purpose and meaning.The second part is the preliminary knowledge, Including some basic theorems.The third part, through four different mathematical models to explain in different research perspective and with variable parameters, the stability of the model of healthy carriers. The main contents of the model summarized as follows.The ?rst model of global stability Bedding-DeAngelis incidence of healthy carriers models. We used Bendixson duration criterion to analyze the global stability of the equilibrium point poison. Introduction of a second additive compound matrix using spectral radius seeking ways to get the basic reproductive number systems. Prove the existence of a positive understanding and local equilibrium point, and explains if the basic reproduction number is less than 1,the equilibrium is globally stable, non-toxic; if the basic reproduction number is greater than one, then the disease is persistent.The second model we consider the time- delay can be modeled with latent period infectious diseases. For epidemic model with Delays,the main issues of concern still is to distinguish whether the expression of disease epidemic threshold, the stability of the equilibrium position, the existence and stability of periodic solutions, sustain ability of the system, as well as relevant control and prevention strategies.Establish an appropriate threshold R0, obtained when R0< 1, the disease-free equilibrium point of the system is globally asymptotically stable if R0> 1, the obtained endemic equilibrium is globally asymptotically stable.Finally, to illustrate the effectiveness of the correctness of the conclusions and methods of mathematical modeling through simulation.The third model we consider the latency Delays simulation of infectious diseases,patients infected with the disease stage. First, we separate the real and imaginary parts of the characteristic equation, the use of reductio ad absurdum argument to the real part of the characteristic roots symbol. In discussing the global stability of the equilibrium point of an in?nite de?nite structure of Liapunov functionals, the corresponding balance in the region discussed global asymptotic stability. Finally, the impact of the model on two delays were simulated to verify the correctness of the conclusions.